We show that first-difference two-stages-least-squares regressions identify non-convex combinations of location-and-period-specific treatment effects. Thus, those regressions could be biased if effects are heterogeneous. We propose an alternative instrumental-variable correlated-random-coefficient (IV-CRC) estimator, that is more robust to heterogeneous effects. We revisit Autor et al. (2013), who use a first-difference two-stages-least-squares regression to estimate the effect of imports from China on US manufacturing employment. Their regression estimates a highly non-convex combination of effects. Our more robust IV-CRC estimator is small and insignificant. Though its confidence interval is wide, it significantly differs from the first-difference two-stages-least-squares estimator.